DHS 17 Electromagnetic Induction (Lecture Slides)

DHS Y6 Physics H2 [Electromagnetic Induction] 18/3/2025 [For Internal Use Only] lim.boonsiong@dhs.edu.sg 1 1 H2 Physics Topic 17: Electromagnetic Induction Key Differences Between Electromagnetism and Electromagnetic Induction 2 Important RulesFocusTopic • Right-hand grip rule (to find direction of B field around a current-carrying wire, produced by a current flowing through a circular loop of wire, and in solenoids • Fleming’s Left-hand Rule (to find the direction of magnetic force on a current-carrying conductor or moving charges in a magnetic field) How currents produce magnetic fields, and how these fields exert magnetic force on moving charges or current-carrying conductors Electromagnetism • Fleming’s Right-hand Rule (to find the direction of induced current) How a changing magnetic field induces an e.m.f. (and a current if the circuit is closed) Electromagnetic Induction 3 Fingers represent … with relevant diagramsRule - Curled fingers = current direction - Thumb = B field direction - Thumb = current direction - Curled fingers = B field direction Right-hand grip rule - First finger = B Field (N to S) - seCond finger = Current direction - ThuMb = Motion (Force) Fleming’s Left-hand Rule - First finger = B Field (N to S) - ThuMb = Motion (movement of conductor) - seCond finger = Induced Current direction Fleming’s Right-hand Rule Quick Reference for the Rules Electromagnetism Electromagnetic Induction 1. Introduction 2. Magnetic Flux and Magnetic Flux Linkage 3. Laws of Electromagnetic Induction • Faraday’s law • Lenz’s law 4. Applications 2 Contents 4 1 2 3 4

DHS Y6 Physics H2 [Electromagnetic Induction] 18/3/2025 [For Internal Use Only] lim.boonsiong@dhs.edu.sg 2 Guiding Question 1 electric current 5 magnetic field produces electric current ??magnetic field produces From Electromagnetism, we learnt that: What about?: What is required for this? Guiding Question 2 6 Can we achieve perpetual motion by invoking the magic of electromagnetism? Electromagnetism is a fundamental force where electric currents generate magnetic fields, influencing current carrying conductors and moving charges, and enabling motors. A changing magnetic field induces a current, which in turn produces another magnetic field, potentially continuing the cycle. Can we use principles of electromagnetism & EMI to create a machine forever without external energy? Cause → Effect RelaƟonships 1. Motion of Magnet • Towards coil: • S-pole → DeflecƟon leŌ, N-pole → DeflecƟon right • Away from coil: • S-pole → DeflecƟon right, N-pole → DeflecƟon leŌ 2. Speed of Movement • Slow push/pull → Small deflecƟon, Fast push/pull → Large deflecƟon • Shows: Induced current ∝ Rate of change of magnetic flux 3. Number of Turns • (10 turns → Small, 20 turns → Larger, 40 turns → Largest) deflecƟon • Shows: Induced current ∝ Number of turns 7 Key Conclusions 1.Magnitude of induced current depends on: – Rate of change of magnetic flux – Number of coil turns 2.Direction of induced current depends on: – Direction of magnet movement – Pole orientation 8 5 6 7 8

DHS Y6 Physics H2 [Electromagnetic Induction] 18/3/2025 [For Internal Use Only] lim.boonsiong@dhs.edu.sg 3 Our Objective: To be able to determine the magnitude and direction of the induced e.m.f. 9 MAGNETIC FLUX DENSITY , B MAGNETIC FLUX,  MAGNETIC FLUX LINKAGE, N define magnetic flux as the product of an area and the component of the magnetic flux density perpendicular to that area a. recall and solve problems using  = BAb. define magnetic flux linkagec. 10 Magnetic Flux Density, BUniform 11 Magnetic Flux,  = B┴ A 1 2 3 2> 3 > 1 Magnetic Flux is defined as the product of an area and the component of the magnetic flux density perpendicular to that area. 12 9 10 11 12

DHS Y6 Physics H2 [Electromagnetic Induction] 18/3/2025 [For Internal Use Only] lim.boonsiong@dhs.edu.sg 4 Magnetic Flux,  Top view Front view 13 B┴ decreases from left to right, so  decreases from left to right Magnetic Flux,  = B A cos B┴ B// B  = (B cos ) A   = B┴ A  is angle between B and normal to Anormal to A Area, A 14 Top view Front view Magnetic Flux defined as the product of an area and the component of the magnetic flux density perpendicular to that area. 15 SI units: weber (Wb) scalar quantity Page 2 cosB A BA    B B cos   The weber is defined as the amount of magnetic flux with density 1 T passing through an area of 1 m2, and 1 T = 1 Wb m−2. Magnetic Flux Linkage, N = N B A cos 16 13 14 15 16

DHS Y6 Physics H2 [Electromagnetic Induction] 18/3/2025 [For Internal Use Only] lim.boonsiong@dhs.edu.sg 5 Magnetic Flux Linkage defined as the product of the magnetic flux passing through the coil and the number of turns on the coil. 17 SI units: weber (Wb) Scalar quantity Page 2 area, A normal B θ cosN NBA  Magnetic flux - examples magnetic flux through the coil = B┴ A = B┴ (πr2) area is half the area of circle 18 magnetic flux through the coil = B┴ (A/2) = B┴ (πr2/2) r magnetic flux through the coil = B┴ (area of smaller circle) = B┴ (πr2) 19 Magnetic flux - examples coil × × × × × × × × × × r 17 18 19

DHS Y6 Physics H2 [Electromagnetic Induction] 26/3/2025 [For Internal Use Only] lim.boonsiong@dhs.edu.sg 1 Example 1 The three loops of wire shown are all in a region of uniform magnetic field. Loop 1 swings back and forth as the bob on a pendulum, loop 2 rotates about a vertical axis and loop 3 oscillates verticall y on the end of a spring. Which loop(s) have a magnetic flux that changes with time? Only loop 2 has a changing magnetic flux as its orientation relative to the field, thus B┴, changes as it rotates. Since the magnetic field is uniform, moving loop 1 back and forth or moving loop 3 up and down does not change the magnetic flux through the loop, that is, the magnetic flux does not depend on the loop’s position. (Here, the magnetic field is directed into the plane of page. It is directed out of page in lecture notes.) 1  = B┴ A Example 2 Initial magnetic flux linkage, (N)i = N B A cos θ = 10(2.0)(0.35) cos 0o = 7.0 Wb Final magnetic flux linkage, (N)f = 0 Change in magnetic flux linkage (N)f – (N)i = 0 – 7.0 = −7.0 Wb A coil of 10 turns and area 0.35 m2 is placed perpendicular to a magnetic field of density 2.0 T as shown in the diagram on the left. Points P and Q are pulled apart until the coil becomes a straight line as shown in the diagram on the right. What is the change in magnetic flux linkage through the coil? 2 DEMO Faraday’s Law and Lenz’s Law 3 infer from appropriate experiments on electromagnetic induction: i. that a changing magnetic flux can induce an e.m.f. ii. that the direction of the induced e.m.f. opposes the change producing it iii.the factors affecting the magnitude of the induced e.m.f. d. recall and solve problems using Faraday’s law of electromagnetic induction and Lenz’slaw e. Electromagnetic Induction Faraday’s Lawof electromagnetic induction states that the induced e.m.f. is directly proportional to the rate of change of the magnetic flux linkage. 4  The negative sign is explained by Lenz’s law. We can drop the sign when we are only interested in the magnitude of the e.m.f.  It indicates that the direction of the induced e.m.f. always opposes the change in magnetic flux linkage. ( ) ( cos )d N d NBA dt dt      1 2 3 4

DHS Y6 Physics H2 [Electromagnetic Induction] 26/3/2025 [For Internal Use Only] lim.boonsiong@dhs.edu.sg 2 Electromagnetic Induction Lenz’s Lawof electromagnetic induction states the induced current or e.m.f. is in a direction to produce effects which oppose the change in magnetic flux that caused it. Lenz’s law is not written separately but combined with Faraday’s law to form an equation. 5 ( ) ( cos )d N d NBA dt dt      The negative sign represents that the direction of the induced current is always such that the magnetic field due to the current opposes the change in the magnetic flux that induces the current. Lenz’s L